Personally I would call a microflow which gets an object passed (when pressing the add new button). If the object is not initial, commit it first and than call the same microflow again to show the screen to create a new one. This way you can keep pressing the add new button and saving the "previous" data.
The solution which I'm proposing would use popups but I think you can also use the workflow method to do this when data is entered on the screen itself. (like Jeff said ;-) ).
What are you trying to do exactly? (Add a new row of data or save the data entered and enter new data?)
You could add an on-change Microflow event that saves your data as it changes this way you can still use the "Add New" but you won't lose your data already entered.